Digital Signal Processing Reference
In-Depth Information
which is the inverse Fourier transform of
S
(
v
). A well-known property of
the Fourier transform pair
s
(
t
) and
S
(
v
) is the uncertainty principle. It
states that the time duration
D
t
of
s
(
t
) and the frequency bandwidth
D
v
of
S
(
v
) are related by
1
2
D
t
D
v
³
(2.3)
where
4
1/2
3
-¥
(
t
-
m
t
)
2
|
s
(
t
)
|
2
dt
D
t
=
¥
-¥
|
s
(
t
)
|
2
dt
4
1/2
3
-¥
(
v-
m
v
)
2
|
S
(
v
)
|
2
d
v
D
v
=
¥
-¥
|
S
(
v
)
|
2
d
v
m
t
m
v
are defined as
and the mean time
and mean frequency
¥
-¥
t
|
s
(
t
)
|
2
dt
m
t
=
¥
-¥
|
s
(
t
)
|
2
dt
¥
-¥
v
|
S
(
v
)
|
2
d
v
m
v
=
¥
-¥
|
S
(
v
)
|
2
d
v
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